Projections in normed linear spaces
نویسندگان
چکیده
منابع مشابه
Remotality and proximinality in normed linear spaces
In this paper, we consider the concepts farthest points and nearest points in normed linear spaces, We obtain a necessary and coecient conditions for proximinal, Chebyshev, remotal and uniquely remotal subsets in normed linear spaces. Also, we consider -remotality, -proximinality, coproximinality and co-remotality.
متن کاملEmbedding normed linear spaces into $C(X)$
It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$. Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology, which is compact by the Banach--Alaoglu theorem. We prove that the compact Hausdorff space $X$ can ...
متن کاملSufficient Enlargements in the Study of Projections in Normed Linear Spaces
The study of sufficient enlargements of unit balls of Banach spaces forms a natural line of attack of some well-known open problems of Banach space theory. The purpose of the paper is to present known results on sufficient enlargements and to state some open problems.
متن کاملSchwarz'S lemma in normed linear spaces.
In this paper we show that any Fréchet holomorphic function mapping the open unit ball of one normed linear space into the closed unit ball of another must be a linear mapping if the Fréchet derivative of the function at zero is a surjective isometry. From this fact we deduce a Banach-Stone theorem for operator algebras which generalizes that of R. V. Kadison.
متن کاملInner Products in Normed Linear Spaces
Let T be any normed linear space [l, p. S3]. Then an inner product is defined in T if to each pair of elements x and y there is associated a real number (x, y) in such a way that (#, y) » (y, x), \\x\\ = (#, #), (x, y+z) = (#,y) + (x, 2), and (/#,y) = /(#, y) for all real numbers /and elements x and y. An inner product can be defined in T if and only if any two-dimensional subspace is equivalen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1950
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1950-0037465-6